At this point, we point out some interesting consequences of Theorem REF .
First of all, \(\Phi \)  cannot be almost injective if \(N<M+1\)  since \(\operatorname{rank}\Phi _{S}+\operatorname{rank}\Phi _{S^\mathrm {c}}\le |S|+|S^\mathrm {c}|=N\) .
Also, in the case where \(N=M+1\) , we note that \(\Phi \)  is almost injective precisely when \(\Phi \)  is full spark, that is, every size-\(M\)  subcollection is a spanning set (note this implies that all of the \(\varphi _n\) 's are nonzero).
In fact, every full spark \(\Phi \)  with \(N\ge M+1\)  yields almost injective intensity measurements, which in turn implies that a generic \(\Phi \)  yields almost injectivity when \(N\ge M+1\)  [1]}.
This is in direct analogy with injectivity in the real case; here, injectivity requires \(N\ge 2M-1\) , injectivity with \(N=2M-1\)  is equivalent to being full spark, and being full spark suffices for injectivity whenever \(N\ge 2M-1\)  [1]}.
Another thing to check is that the condition for injectivity implies the condition for almost injectivity (it does).
